Representative Crawford faces seven counts of failure to file tax returns. Authorities say Crawford did not file state income taxes on time from 2004 to 2007.
He denies the charges.
The jury started deliberating the case at 4:30 p.m.
Last week, Judge Cooper refused to throw out tax evasion charges against Crawford, who said it was impossible to get a fair trial because Gov. Nikki Haley discussed his case to try to make her tax problems seem less serious.
The Associated Press Contributed to this report.